Q. 18 B5.0( 3 Votes )

# If 15 cot A=18, find sin A and sec A.

Answer :

Given: 15 cot A = 8

And we know that,

Or

Let,

Side adjacent to angle A =AB = 8k

The side opposite to angle A =BC = 15k

where k is any positive integer

Firstly we have to find the value of AC.

So, we can find the value of AC with the help of Pythagoras theorem

⇒ (AB)^{2} + (BC)^{2} = (AC)^{2}

⇒ (8k)^{2} + (15k)^{2} = (AC)^{2}

⇒ (AC)^{2} = 64 k^{2} +225 k^{2}

⇒ (AC)^{2} = 289 k^{2}

⇒ AC =√289 k^{2}

⇒ AC =±17k

But side AC can’t be negative. So, AC = 17k

Now, we will find the sin θ

Side opposite to angle θ = BC = 15k

and Hypotenuse = AC = 17k

So,

Now, we know that,

The side adjacent to angle θ = AB =8

Hypotenuse = AC =17

So,

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